K-theoretic boson-fermion correspondence and melting crystals

Abstract

We study non-Hermitian integrable fermion and boson systems from the perspectives of Grothendieck polynomials. The models considered in this article are the five-vertex model as a fermion system and the non-Hermitian phase model as a boson system. Both of the models are characterized by the different solutions satisfying the same Yang-Baxter relation. From our previous works on the identification between the wavefunctions of the five-vertex model and Grothendieck polynomials, we introduce skew Grothendieck polynomials, and derive the addition theorem among them. Using these relations, we derive the wavefunctions of the non-Hermitian phase model as a determinant form which can also be expressed as the Grothendieck polynomials. Namely, we establish a K-theoretic boson-fermion correspondence at the level of wavefunctions. As a by-product, the partition function of the statistical mechanical model of a 3D melting crystal is exactly calculated by use of the scalar products of the wavefunctions of the phase model. The resultant expression can be regarded as a K-theoretic generalization of the MacMahon function describing the generating function of the plane partitions, which interpolates the generating functions of two-dimensional and three-dimensional Young diagrams.

v4, 31 pages, 14 figures

References in corpus (3)

• Vertex models, TASEP and Grothendieck polynomials
• G/G gauged WZW model and Bethe Ansatz for the phase model
• Phase model expectation values and the 2-Toda hierarchy

Cited by in corpus (25)

• Colored five-vertex models and Lascoux polynomials and atoms
• Riemann surfaces for KPZ with periodic boundaries
• Double Grothendieck polynomials and colored lattice models
• Grothendieck polynomials and the Boson-Fermion correspondence
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• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Riemann surface for TASEP with periodic boundaries
• Free-fermions and skew stable Grothendieck polynomials
• Integrability approach to Feher-Nemethi-Rimanyi-Guo-Sun type identities for factorial Grothendieck polynomials
• Crystal structures for symmetric Grothendieck polynomials
• Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice
• KPZ fluctuations in finite volume
• Quantum integrable combinatorics of Schur polynomials
• Determinant formulas for the five-vertex model
• Riemann surfaces for integer counting processes
• Dual wavefunction of the symplectic ice
• Free fermions and Schur expansions of multi-Schur functions
• Neutral-fermionic presentation of the $K$-theoretic $Q$-function
• On the eigenfunctions for the multi-species q-Boson system
• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• A class of partition functions associated with $E_{\tau ,\eta }(g{l}_3)$ by Izergin-Korepin analysis
• Quasi-solvable lattice models for ${\mathrm{Sp}}_{2n}$ and ${\mathrm{SO}}_{2n+1}$ Demazure atoms and characters
• Scalar products of the elliptic Felderhof model and elliptic Cauchy formula
• Free fermionic probability theory and K-theoretic Schubert calculus
• Integrable models and $K$-theoretic pushforward of Grothendieck classes